Using the binomial distribution, it is found that there is a 0.0328 = 3.28% probability that at least 2 of them choose the same quote.
<h3>What is the binomial distribution formula?</h3>
The formula is:
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem, we have that:
- There are 6 students, hence n = 6.
- There are 20 quotes, hence the probability of each being chosen is p = 1/20 = 0.05.
The probability of one quote being chosen at least two times is given by:
In which:
P(X < 2) = P(X = 0) + P(X = 1).
Then:
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.7351 + 0.2321 = 0.9672.
0.0328 = 3.28% probability that at least 2 of them choose the same quote.
More can be learned about the binomial distribution at brainly.com/question/24863377
Every 56 seconds, the radioactive substance is divided in half.
224 / 56 = 4
We need to cut the substance in half 4 times.
896 / 2 = 448
448 / 2 = 224
224 / 2 = 112
112 / 2 = 56
After 224 seconds, there will be 56 grams of the radioactive substance left over
Deductive reasoning is one that necessarily follows, not one that likely follows (this would be an inductive reasoning).
Here the important information is that all squares are also parallellograms, which means that they also necesarily have all the properties of the parallelogram - the correct answer is D.
<span> To get an explicit formula, we need to find an expression which gives the n-th term without having to compute earlier terms in the sequence. Looking at the numbers, and from the recursive formula, we see that the sequence is built by subtracting n from the previous term. This is similar to the triangular number sequence 1,3,6,10,15,... which has the explicit formula a_n = n(n+1)/2. In our case we are subtracting n from the previous term, so we multiply by -1/2 instead of 1/2. However, we also need to add a constant term to reproduce the numbers of the sequence. We can write a_1 = -1(2)/2 + c = 8. Therefore, c = 9.
So the explict formula is:
a_n = -n(n+1)/2 + 9</span>
1)To construct a line parallel to line l and passing through point P our first step is to join the point and line and then draw angles in such a way so that corresponding angles are equal.
Option B is the correct construction of a line parallel to line l and passing through point P.
2) To Construct the perpendicular line to line DE at point F we cut an arc from point F to line DE in such a way it cuts line DE at two points .From these two points we draw arcs which cut each other .
Option C is the correct option to Construct the perpendicular line to line DE at point F.
3) To Construct a perpendicular from the given line segment that passes through the given point we cut two arcs on top and bottom of line segment.
Option B is the right answer.
